Data Compression(2)

7/31/2019 Data Compression(2)

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1

IMAGE COMPRESSION

TECHNIQUES

S.Esakkirajan

Assistant Professor

I&CE DepartmentPSG College of Technology

Coimbatore


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2

Topics of Presentation

Need for image compression

Transform based image compression

Vector Quantization

Image Compression Standards


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3

What is Compression?

Compact representation.

Representing the data with minimum

number of bits.


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4

Need for Compression

To minimize the storage space

To enable higher rate of data transfer


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Philosophy of Compression

5

DATA

INFORMATION

DATA=USEFULDATA + UNWANTED DATA

Unwanteddata

RedundantData

Irrelevant data

Useful information = Data[Redundant + Irrelavant data]


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6

Philosophy of Compression(Cont.,)

H2OH2O
http://www.google.co.in/imgres?imgurl=http://www.hort.purdue.edu/ext/senior/fruits/images/large/orange3.jpg&imgrefurl=http://www.hort.purdue.edu/ext/senior/fruits/orange1.htm&usg=__0w_U6Cnc7z8xBef1TvusLzCDhtk=&h=480&w=640&sz=53&hl=en&start=33&itbs=1&tbnid=aMhGF8c-jF9kvM:&tbnh=103&tbnw=137&prev=/images%3Fq%3Dbunch%2Bof%2Borange%2Bfruits%26start%3D18%26hl%3Den%26sa%3DN%26gbv%3D2%26ndsp%3D18%26tbs%3Disch:1


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Classification of Redundancy

Redundancy in Image

SpatialRedundancy

PsychoVisualRedundancy

CodingRedundancy


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8

Classification of Compression

Techniques

Original DataCompressedData

Lossless

Original Data

Approximated


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99

Transform Coding

Transform QuantizationEntropyCoding

InputImage

Compressedbitstream

InverseTransform

InverseQuantization

EntropyDeCoding

ReconstructedImage

Compressedbitstream

Image Encoding

Image Decoding


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10

Transform

Compact energy into a few coefficients.

Decorrelate (reduce linear dependence)among coefficients.

KL transform, DCT, Wavelet.


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KL transform

11

Input Image

Partition of the imageinto blocks

Compute the Mean

Compute the

Covariance Matrix

Eigen Vector of theCovariance Matrix


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Discrete Cosine Transform

Fourier basis: Complex exponential (ejt )

cos(t)= 0.5[ejt +e-jt ]

Symmetrical extension of DFT

12


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DCT (Cont.,)

13

n

xe[n]

n

x[n]

xe[n]

n


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DCT (Cont.,)

14

otherwise

Nk

Nk

N

kn

N

knnnx

kkC

N

n

N

nx

,0

10

10,

2

12cos

2

12cos],[4

],[22

11

2

22

1

11

21

1

0

1

021

1

1

2

2

otherwise

Nk

Nk

N

kn

N

knkkCkwkw

NNnnx

N

k

N

k

x

,0

10

10,

2

12cos

2

12cos],[][][

1

],[22

11

2

22

1

11

21

1

0

1

0

2211

2121

1

1

2

2


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Wavelet Transform

Oscillatory function of finite duration.

CWT and DWT

Multi-resolution Analysis

Wide variety of basis function

15


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DWT - Implementation

16

LPF

HPF

2

2

LPF 2

HPF 2

LPF 2

HPF 2

InputImage

Column

processing

Rowprocessing

LL

LH

HL

HH


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SUBBAND DECOMPOSITION

0

0

0

0 0

0

0 0

0

00

0

0

0

0

0

0 0 0

0

0 0

0

0

0 0

0

0

0 1

1

0

1

11

11

1

1

1

0 0

1

0

1

1

1

1

1

0 0 00 0 0 0

0

0

0

0

0

0

0

0

Low pass filter is ,

INPUT IMAGE

RESULTANT IMAGE

AFTER ROW

PROCESSING

0 0 0

0 0

0

0

0

0

0

0

0

0

0

0

0 0

0

0

0

00

0 0


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Step 1b :COLUMN PROCESSING OF THERESULTANT

0

0

00 0

0 0

0

0

0 0

0

0

000

0

0

0

0

0

0

0

0

LOW PASS FILTERED IMAGE

LL SUBBAND

0 0 0

0

0

0 0 0

0

0

0

0

2 2

2 2


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STEP 2:TO FIND THE SUBBAND LH

0

0

00 0

0 0

0

0

0 0

0

0

000

0

0

0

0

0

0

0

0

LOW PASS FILTERED IMAGE ALONG ROW

THE LH SUBBAND

0 0 00

0

0

0

0 0

0

00

0

0

0

0


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STEP 3:TO FIND HL SUBBANDSTEP 3a :HIGH PASS FILTERING ALONG ROW

0

0

0

0 0

0

0 0

0

00

0

0

0

0

0

0 0 0

0

0 0

0

0

0 0

0

0

0 1

1

0

1

11

11

1

1

1

0 0

1

0

1

1

1

1

1

0 0 00 0 0 0

0

0

0

0

0

0

0

0

IMPUT IMAGE HIGH PASS FILTERED

IMAGE

0 00 0

0

0

0

0

0

0

0

0

0

0

0

0000

0

0

00

0

0

0

0

00

00

0


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STEP 3B: LOW PASS FILTERING OFRESULTANT IMAGE ALONG COLUMN

0 00 0

0

0

0

0

0

0

0

0

0

0

0

0000

0

0

00

0

0

0

0

00

00

0

HIGH PASS FILTERED IMAGE

OBTAINED IN STEP 3a

HL SUBBAND

0 0 00

0

0

0

0 0

0

00

0

0

0

0


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STEP 4 :TO FIND HH SUBBAND (HIGH PASS FILTERING

ALONG ROW & THEN HIGH PASS FILTERING ALONGCOLUMN)

0 00 0

0

0

0

0

0

0

0

0

0

0

0

0000

0

0

00

0

0

0

0

00

00

0

HIGH PASS FILTERED IMAGEHH SUBBAND

0 0 00

0

0

0

0 0

0

00

0

0

0

0


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STEP 5:DECOMPOSITION OF INPUT IMAGE INTOFOUR SUBBANDS LL,LH,HL,HH

0

0

0

0 0

0

0 0

0

00

0

0

0

0

0

0 0 0

0

0 0

0

0

0 0

0

0

0 1

1

0

1

11

11

1

1

1

0 0

1

0

1

1

1

1

1

0 0 00 0 0 0

0

0

0

0

0

0

0

0

INPUT IMAGE

FIRST LEVEL

WAVELET

DECOMPOSITION

00 00

0

0

0

2 2

0

2 2

0

0

0

0

00 00

0

0

0

0 0

0

0 0

0

0

0

0

00 00

0

0

0

0 0

0

0 0

0

0

0

0

00 00

0

0

0

0 0

0

0 0

0

0

0

0

LL LH

HL HH

00 00

0

0

0

2 2

0

2 2

0

0

0

0

00 00

0

0

0

0 0

0

0 0

0

0

0

0

00 00

0

0

0

0 0

0

0 0

0

0

0

0

00 00

0

0

0

0 0

0

0 0

0

0

0

0


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SECOND LEVEL DECOMPOSITION

00 00

0

0

0

2 2

0

2 2

0

0

0

0

00 00

0

0

0

0 0

0

0 0

0

0

0

0

00 00

0

0

0

0 0

0

0 0

0

0

0

0

00 00

0

0

0

0 0

0

0 0

0

0

0

0

SECOND LEVEL

WAVELET

DECOMPOSITION

01 01

1

0

0

1 0

0

0 0

0

0

0

0

0-1 0-1

-1

0

0

-1 0

0

0 0

0

0

0

0

0-1 0-1

-1

0

0

-1 0

0

0 0

0

0

0

0

0-1 0-1

-1

0

0

-1 0

0

0 0

0

0

0

0

LL

HL HH

LH

01 01

1

0

0

1 0

0

0 0

0

0

0

0

0-1 0-1

-1

0

0

-1 0

0

0 0

0

0

0

0

0-1 0-1

-1

0

0

-1 0

0

0 0

0

0

0

0

0-1 0-1

-1

0

0

-1 0

0

0 0

0

0

0

0

FIRST LEVEL DECOMPOSED IMAGE


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2525

Properties of Wavelet Filters

Compact support

Symmetric

Vanishing Moment

Regularity


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Quantization

26

Approximation.

Mapping large set of values to small set of

values.

It is a non-linear and irreversible process

Range of Marks Grade

0 to 49 F

50-54 E

55-59 D

60-69 C

70-79 B

80-89 A

90-100 S


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Quantization Techniques - Classification

Quantization

VectorQuantization

EmbeddedQuantization

ScalarQuantization

Uniform

Non-

Uniform

Mid-tread Mid-rise

EZW SPIHT SPECK

TSVQ MSVQ HVQ


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Vector Quantization

Search

Engine

..

..

..

Codebook Indices

The Encoder

Output

Vector

..

..

..

Indices Codebook

The Decoder

Channel

Input

Vector


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2 4 6 8

10 11 16 15

9 3 1 7

12 14 13 5

Consider an input image

of size 4 by 4

Choose the dimension

as two

16

1

Here Maximum value=16

Minimum value =1

Dynamic range=Maximum-Minimum

=16-1=15


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4 8 12 160

4

8

12

16

*

*

*

*

*

*

*

*

* *

* *

*

*

*

*

C12

C8

C4

C0

C13

C9

C14 C15

C10 C11

C5 C6 C7

C1 C2 C3

(2,2)

(2,6)

(2,10)

(2,14)

(6,2)

(6,6)

(10,6)

(14,6)

(10,2)

(10,6)

(10,10)

(14,2)

(14,6)

(14,10)

(14,14)(14,10)

In this example,

rate(R)=2,dimension(L)=2

Number of code

vectors=2^(R*L)=16

Code vectors are

C0 to C15

Fixing the interval

LR

geDynamicRanInterval

In our case

interval=4

C0 to C15 is

obtained using

Centroid Method


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2 4 6 8

10 11 16 15

9 3 1 7

12 14 13 5

0 4 8 16

4

8

12

16

12

*

*

* * *

*

*

*

* * *

*

*

*

* *

.

.

..

.

.

.

.

Mapping of Input Image Vector to Code Vector


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0 4 8 16

4

8

12

16

12

*

*

* * *

*

*

*

* * *

*

*

*

* *

(1,7)

(6,8)

(2,4)

(10,11)

(12,14) (16,15)

(9,3) (13,5)(2,6) (6,6)

(2,2)

(10,10)

(14,14)(14,14)

(10,2)

(14,6)

Adjust the Input Vectors to fall into one of the

Code Vectors


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33

12(2,4)

Input Image

Vectors

Transmitted

Indices

(6,8)

(10,11)

(9,3)

(1,7)

(16,15)

(12,14)(13,5)

9

6

3

11

3

8

14


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34

2 2 6 6

10 10 14 14

10 2 2 6

14 14 14 6

Original image Reconstructed image

2 4 6 8

10 11 16 15

9 3 1 7

12 14 13 5

12 9 6 3 14 8 113

Si l C ffi i tTransform


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Detachment from Attachment

Attachment

Signal CoefficientTransform

Decorrelation

Coefficients are correlated


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Embedded Quantization

Progressive Quantization

(a) EZW (b) SPIHT (c) SPECK etc

Starting point Wavelet Coefficients

Parent-child relationship in waveletdomain

36

T i l i i EZW


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Terminologies in EZW

Root node/ Parent node

Child node

(a) Significant Positive (SP)

(b) Significant Negative (SN)

(c) Zero-tree Root (ZR)

(d) Isolated Zero (IZ)

Dominant Pass and Refinement pass

37

T i l i i EZW (C t )


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Terminologies in EZW (Cont.,)

38

R C1

C3C2

X X

X X

X X

X X

X X

X X

Maximum Coefficient Value Cmax= R

T0

= 2floor(log2(Cmax))Magnitude of the coefficient > Magnitude of Threshold = SPMagnitude of the coefficient > Magnitude of Threshold = SNMagnitude of the coefficient < Magnitude of Threshold &

ALL Descendents magnitude Threshold = IZ

Computation ofThreshold

EZW Ill t ti


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EZW - Illustration

39

34 0

00

1 -1

1-1

4

-4

-4

4

10 -6

6 -10

T0 = 2floor(log2(34)) = 25 = 32

Dominant Pass

34>32 = SP ZR ZR ZR Ls = {34}

Data transmitted: Threshold, SP, ZR,ZR,ZR

48 0

00

0 0

00

0

0

0

0

0 0

0 0

Reconstructed value: (3/2)T0 =48

Refinement Pass

Ls Reconstructed value = -14

Correction term sign:

Correction term = (T0/4) = (32/4) = 8Corrected value= 48-8 = 40

40

EZW Illustration


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EZW - Illustration

40

40 0

00

0 0

00

0

0

0

0

0 0

0 0

X

Dominant Pass

Threshold value T1 = (T0/2) =16

zr zr zr Ls = {34}

0

00

0 0

00

0

0

0

0

0 0

0 0

40

Refinement Pass

Correction term sign:

Ls Reconstructed value =- 6

Correction term = (T1/4) = (16/4) = 4

36


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Runlength Coding

0(12)

0(12)

0(12)

0(12)

0(12)0(5)1(2)0(5)

0(5)1(2)0(5)

0(12)

0(12)

0(12)0(12)

0(12)


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Runlength Coding

0(12)

0(12)

0(12)

0(12)

0(12)0(5)1(2)0(5)

0(5)1(2)0(5)

0(12)

0(12)

0(12)0(12)

0(12)


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Runlength limitation

HUFFMAN CODE


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HUFFMAN CODE

Based on probability and entropy

Basic philosophy of Huffman code

Variable length code

Prefix code

H ff d E l


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Huffman code - Example

Symbol Probability

1/2

1/4

1/8

1/8

Spade

HeartDiamond

Club


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Huffman code Example (Cont.,)

Code Symbol Probability Step 1 Step 2

1/2

1/4

1/8

1/8

1/4

1/4

1/2

1/2

1/2 (0)

(1)

(0)

(1)

(0)

(1)

0

10

110

111


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LOSSLESS DPCM

Signal to be Transmitted


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EntropyEncoder

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P f I di


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Performance Indices

Compression Ratio (CR)

Bitrate

PSNR

82

filecompressedtheofsize

fileoriginaltheofsizeCR

imagetheinpixels

filecompressedtheofsizebpp

MSE

1PSNRb 2

10

12log0

JPEG


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JPEG

JPEG CODEC

InputImage

FDCT Quantizer EntropyEncoder

Channel

IDCT DequantizerEntropy

Decoder

DCT based Decoder

DCT based Encoder8 X 8 blocks

zigzag

Reverse

zigzag

JPEG MODES


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JPEG MODES

Sequential Mode

Progressive Mode

Hierarchical Mode

Lossless Mode

D b k f JPEG


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Drawback of JPEG

Artifact

Blocking artifact Ringing artifact

Due to block processing Sharp oscillation or

ghost shadows

Bl ki tif t


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Blocking artifact

JPEG 2000


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JPEG 2000

Wavelet Trasform.

Compress once and decode many times

Supports different scalability

Supports Region of Interest Coding

Error Resilience

JPEG 2000


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J G 000

2D FDWTScalar

Quantization

Block based

Arithmetic

coding

2D IDWTInverse

Quantization

Block based

Arithmetic

decoding

Bitstream j2k3HH

3HL

3LH

2HL

2LH

1HL

2HH

1LH 1HH

0LL

Rate-distortion

Allocation

optimisation

Progressive Transmission by


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g y

resolutionCompressed Image bitstream



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Compressed Image bitstream

g y

position



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Compressed Image bitstream

g y

components


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Image Segmentation

Subdivide the image into its componentregions

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Segmentation Algorithms

Discontinuity Similarity

Robert Prewitt Sobel Region

growing

Region

Splitting

Split and

Merge

Image Segmentation Example


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Image Segmentation - Example

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Data Compression(2)

Documents

Transcript of Data Compression(2)